The undirected de Bruijn graph: fault tolerance and routing algorithms
M.A. Sridhar · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · 1992
The undirected version of the de Bruijn graph, also called the shift-and-replace graph, has N=k/sup n/ vertices, maximum degree k, and minimum degree k-2. A.H. Esfahanian and S.L. Hakimi (1985) have shown that this graph has diameter n=log/sub k/N, connectivity 2k-2, and has an increase in diameter of at most log/sub k/n+4 in the presence of up to 2k-3 fault vertices. The author tightens this bound significantly. It is shown that the increase in the diameter of this graph is at most log/sub k/log/sub phi /n+6+log/sub k/5, where phi is the golden ratio. The methods used draw upon the theory of string overlaps and the theory of finite automata.>